A hybrid direction algorithm for solving linear programs

Bibi, Mohand Ouamer; Bentobache, Mohand

doi:10.1080/00207160.2014.890188

Cited by 11 publications

(9 citation statements)

References 9 publications

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“…In [15], the Cauchy formula for solving systems of linear differential equations is used to transform the linear optimal control problem into an equivalent problem, then discretization is performed to get a linear programming problem which is solved using the adaptive method. Recently in [16], the Cauchy formula is used with discretization to transform the original linear optimal control problem into a linear optimization problem which is solved with the hybrid direction algorithm proposed in [17]. In [18], the Euler discretization formula 282 OPTIMAL CONTROL OF A RECTILINEAR MOTION OF A ROCKET is first applied for the initial linear optimal control problem, then the obtained optimization problem is solved with the fmincon function of Matlab.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a rectilinear motion of a rocket

Aliane

Moussouni

Bentobache

2020

Stat., optim. inf. comput.

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In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.

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Section: Introductionmentioning

confidence: 99%

Optimal control of a rectilinear motion of a rocket

Aliane

Moussouni

Bentobache

2020

Stat., optim. inf. comput.

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“…Modern researchers also propose modified linear programming algorithms that either formally simplify (Belahcene, Marthon & Aidene, 2018) or speed up the solution of the problem (Bibi & Bentobache, 2015).…”

Section: Introductionmentioning

confidence: 99%

Optimum planning use of equipment in agriculture

Zaynagabdinov

Gabitov

Bakiev

et al. 2020

JIEM

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Purpose: to reduce operating costs when performing agricultural mechanized work.Design/methodology/approach: The development of the desired economic and mathematical model of the optimal MTA distribution by type of work is based on the above condition it is necessary to plan the work of not tractor brands indicating their number, but each tractor individually.Findings: It is known that the availability of equipment varies during the season, so it was studied in dynamics. In this regard, to solve this problem, neural-network simulation was first used. As a result of the search, a network of the type of radial basis function was obtained that best describes these dependenciesResearch limitations/implications: the authors developed a fundamentally new mathematical model for optimizing the use of technology, which, unlike existing ones, allows to:- plan the operation of each tractor individually;- designate the so-called “mandatory tractors”, that is, those that the user, at his discretion, would like to assign to a particular operation or vice versa, would like the tractor operator not to work on this operation.Originality/value: Thus, the scientific novelty of the work performed are:- a technique for operational planning of work and increasing the efficiency of using the MTA, taking into account the technical condition of the tractors, the specific conditions for their functioning and the work experience of the machine operator.- a mathematical model for solving the problem of the optimal distribution of MTA by type of work and the mathematical apparatus for its implementation;- a technique for adjusting the performance of the MTA, taking into account the experience of the tractor driver, the service life and technical readiness of the tractor.

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“…In References 10‐13, a new algorithm for solving linear programming problems with bounded variables was developed. This algorithm uses the concept of hybrid direction in order to move from one feasible solution to a better one.…”

Section: Introductionmentioning

confidence: 99%

“…Later, this algorithm is generalized for solving convex quadratic programs 14 and optimal control problems 15 . In this work, we propose a new hybrid direction, which gives a better local improvement for the objective function than the AMHD algorithm developed previously in Reference 13. The stopping criterion of the AMHD algorithm is based on a quantity called optimality estimate, so it gives only optimal solutions and the support is changed using the short step rule.…”

Section: Introductionmentioning

confidence: 99%

A new method with hybrid direction for linear programming

Djeloud

Bentobache

Bibi

2020

Concurrency and Computation

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Summary In this work, we propose a new algorithm for solving linear programs. This algorithm starts by an initial support feasible solution, then it moves from one feasible point to a better one following a new hybrid direction. The constructed direction gives a better local improvement of the objective function than the direction of the adaptive method with hybrid direction (AMHD) algorithm proposed in Bibi MO, Bentobache M. A hybrid direction algorithm for solving linear programs. International Journal of Computer Mathematics, 2015; 92(2):200‐216. In order to stop the algorithm, a suboptimality criterion is used and the long step rule is developed for changing the current support. The proposed algorithm is implemented with C++, then a numerical study is conducted on randomly generated test problems and some instances of an optimal control problem. The obtained numerical results show that our algorithm is competitive with AMHD and the primal simplex algorithm of GNU linear programming kit (GLPK).

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A hybrid direction algorithm for solving linear programs

Cited by 11 publications

References 9 publications

Optimal control of a rectilinear motion of a rocket

Optimal control of a rectilinear motion of a rocket

Optimum planning use of equipment in agriculture

A new method with hybrid direction for linear programming

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